Explicit <i>N</i>th order solutions of Fokas–Lenells equation based on revised Riemann–Hilbert approach
Yongshuai Zhang, Deqin Qiu, Jingsong He
Abstract
We develop a revised Riemann–Hilbert problem (RHP) to the Fokas–Lenells (FL) equation with a zero boundary condition, satisfying the normalization condition, and the potential of the FL equation is recovered from the asymptotic behavior of RHP when the spectral parameter goes to zero. Under the reflection-less situation, we consider the RHP with 2N simple poles and two Nth order poles, respectively, and obtain the explicit formulas of Nth order soliton and positon solutions. As applications, the first-order soliton, the second-order soliton, and positon are displayed. Additionally, the collisions of N solitons are studied, and the phase shift and space shift are displayed.
Topics & Concepts
MathematicsRiemann hypothesisNormalization (sociology)SolitonMathematical analysisOrder (exchange)Hilbert spaceBoundary value problemZero (linguistics)Mathematical physicsPure mathematicsQuantum mechanicsPhysicsNonlinear systemAnthropologyFinancePhilosophyLinguisticsEconomicsSociologyNonlinear Waves and SolitonsNonlinear Photonic SystemsAlgebraic structures and combinatorial models